High-Precision Position Tracking Control with a Hysteresis Observer Based on the Bouc–Wen Model for Smart Material-Actuated Systems

Round 1

Reviewer 1 Report

The manuscript carries an interesting topic in the field. Experimental results are interesting and exhibit good results, but some minor issues need to be addressed before making further decisions.

- What is the main contribution of your paper? Is it considering Bouc-Wen Hysteresis Observer design for Smart Material-Actuated Systems?

-Please show the control signals applied to the system. It is very important from a practical implementation point of view.

-Please discuss sampling time. You should explain a justification why it is appropriate. For instance, it can be mentioned that "the sampling period is less than 10% of the step response settling time for adequate recognition of the system dynamics.

- Please compare the comparisons presented in tables 1 and 2 by percentage. It is better for the readers. Furthermore, some performance indexes the same as those defined in [10.1109/ICIT.2018.8352185] should be utilized for the contro input.

good

Author Response

Reviewer #1: The manuscript carries an interesting topic in the field. Experimental results are interesting and exhibit good results, but some minor issues need to be addressed before making further decisions.

1. What is the main contribution of your paper? Is it considering Bouc-Wen Hysteresis Observer design for Smart Material-Actuated Systems?

Reply 1: Thank you for your constructive recommendation. In our work, we treat the hysteresis system as a whole, rather than a linear system with a hysteresis perturbation, which is different from existing state estimation methods. We estimate the hysteresis state without requiring knowledge of the initial state of the system, which greatly facilitates control implementation. The stability of the output-feedback tracking controller with the proposed high-gain hysteresis observer is then proven by constructing a Lyapunov function. The contributions are explained on page 2 of the revised manuscript.

Additionally, the hysteresis observer is designed based on the Bouc-Wen model, but to avoid confusion with a physical phenomenon, it is defined as a high-gain observer based on the Bouc-Wen model.

2. Please show the control signals applied to the system. It is very important from a practical implementation point of view.

Reply 2: Thank you very much for your insightful comment, it is a great suggestion. The control signals applied to the system have been given in the revised manuscript. It is shown in Fig 7 and 8.

3. Please discuss sampling time. You should explain a justification why it is appropriate. For instance, it can be mentioned that "the sampling period is less than 10% of the step response settling time for adequate recognition of the system dynamics [10.1007/s11071-017-3623-x], [10.1109/ICIT.2018.8352185]

Reply 3: Thank you very much for your comments. In this work, the sampling time is set as 0.0002s in the process of experiment. When the sampling time is set to larger, the output of piezoelectric actuated stage can introduce some external noise. In the actual experiment, we utilized the maximum computing power of the STM32 chip to maintain the sampling time at 0.0002s. According to your suggestion in reference [10.1007/s11071-017-3623-x] and [10.1109/ICIT.2018.8352185], we find that when the reference trajectory is a step signal, both ESO and HPSO have a “peak” phenomenon, which leads to the instability of the whole control system. In the future, we will study the “peak” phenomenon of the state observer and solve this problem. In the revised manuscript, we have added a description of the sampling time. In the future study, the “peak” phenomenon will be explored. Please see two parts revised on page 9 and 12 in the new manuscript.

4. Please compare the comparisons presented in tables 1 and 2 by percentage. It is better for the readers. Furthermore, some performance indexes the same as those defined in [10.1109/ICIT.2018.8352185] should be utilized for the control input.

Reply 4: Thank you very much for your great suggestions. We have added the comparisons presented in tables 1 and 2 by percentage in the revised manuscript. In addition, we have studied and referenced the control input description in [10.1109/ICIT.2018.8352185] and referenced it. Please see tables 1 and 2 and the red text on the page 11 of the revised manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors,

My remarks and review points are listed in the attachment. 

Kind Regards

Comments for author File: Comments.pdf

English should be polished

Author Response

Reviewer #2: The authors of this manuscript present a state observer to estimate the unmeasurable states of hysteresis systems represented by a Bouc-Wen model for piezoelectric actuator based precision stages. The manuscript is very interesting. However, this paper must be improved before it can be published. I strongly suggest that the authors check the format and grammatic again. My remarks and questions are listed below;

1. If we compare table 1 and table 2 that, there is not a complete matching between simulations and experiments. Tracking error with the method of PHSO is significantly smaller than the one with the method of ESO (differences are more than 10 times). But the experiments show that there is not so much difference between the PHSO and ESO (differences are approximately 2 times). Please explain the reason of this mismatching. Please insert this explanation in the manuscript.

Reply 1: Thanks for your great questions. It is extremely helpful for improving our manuscript. In the previous manuscript, the travel range of the desired reference signal are different between the simulation and experiment. This is one reason for the inconsistency between simulations and experiments results. Now, we have revised this problem. In addition, the tracking error with the method of PHSO is significantly smaller than the one with the method of ESO, which is improved about 80% in simulation. However, the experiments show that there is not so much difference between the PHSO and ESO, which is improved about 40%. This is because the external disturbances and model uncertainties have an impact on the performance of the controller. For example, the hysteresis part of PHSO based on the Bouc-Wen model cannot describe the actual hysteresis characteristics of the piezoelectric actuated stage. However, the hysteresis part of the PHSO method is consistent with piezoelectric systems (that is replaced by the obtained Bouc-Wen model) in simulation. That is another reason. We have added the explanation in the new manuscript. Please see the page 11 of the revised manuscript.

2. You did not show any simulations with triangle trajectory. But you have experiments with triangular trajectory. In order to get a better comparison, one needs simulation of triangular trajectory as well. Please add the simulation of it and put the results in table 1.

Reply 2: Thank you very much for your great suggestions. We have added the simulations with triangle trajectory in the new manuscript. Please see Fig. 5 in the revised manuscript.

3. Other remarks and corrections are as follows; Introduction: Your focus in this paper is high-precision position tracking control with a Bouc-Wen hysteresis observer for smart material-actuated systems. Therefore, you should mention about the nonlinearity of the piezoelectric actuators like hysteresis which is time and rate dependent. You should mention these nonlinearities in the introduction with some references. You could use following papers about nonlinearities and their time dependency of the piezoelectric actuators;

[xx] Delibas, B.; Arockiarajan, A.; Seemann, W. Rate dependent properties of perovskite type tetragonal piezoelectric materials using micromechanical model. Int. J. Solids Struct. 2006, 43, 697–712.

[xx] Damjanovic, Dragan. "Hysteresis in piezoelectric and ferroelectric materials." Science of hysteresis (2006): 337-465.

Reply 3: Thank you very much for this constructive recommendation. We have added some discussion about the rate-dependency of the smart material systems according to your suggestions. Please the introduction part in the revised manuscript.

4. Line 3: „dam-per“ should be “damper”.

Reply 4: Thank you very much for this constructive recommendation. We are sorry for the trouble brought to you by our inadequate language. In the revised manuscript, we have tried to polish them as many as possible, including the spelling mistakes, typo errors and so on. We hope they won’t puzzle the reader any more.

5. Please insert Figure 1 in the section of simulation results not before it.

Reply 5: Thank you very much for this constructive recommendation. We have revised the manuscript according to your suggestion.

6. Figures 3 and 4: Axes are not in the same size. Axis title for the y-axis is written bigger than the one in x-axis. Additionally, styles are not same. Please modify the figure accordingly. Please obey the rules of academic writing.

Reply 6: Thank you very much for your constructive suggestions. We have redrawn the Fig. 3 and 4 to obey the rules of academic writing in the revised manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

1. The reviewer suggests adjusting the title to "... with a Hysteresis Observer Based on the Bouc-Wen Model for .....". Using 'Bouc-Wen Hysteresis Observer' may confuse readers into thinking it refers to a specific physical phenomenon rather than a mathematical model.

2. According to Lyapunov function, the derivative of this function must be negative definite to ensure local asymptotic stability. However, the proof presented on pages 4 and 5 only demonstrates that the derivative of the chosen Lyapunov function can be constrained to a bounded number. Without specific conditions provided, it is challenging to ascertain that it is indeed negative definite. The authors should ensure that this step can be proven so that the observer's stability, as claimed, can be guaranteed. 

3. The amplitudes in the experimental setup do not match those in the simulation. It may be necessary to ensure consistency in conditions between the simulation and the experiment.

Author Response

Reviewer #3：

1. The reviewer suggests adjusting the title to "... with a Hysteresis Observer Based on the Bouc-Wen Model for .....". Using 'Bouc-Wen Hysteresis Observer' may confuse readers into thinking it refers to a specific physical phenomenon rather than a mathematical model.

Reply 1: Thank you very much for your constructive suggestions. We have revised the title “High-Precision Position Tracking Control with a Hysteresis Observer Based on the Bouc-Wen Model for Smart Material-Actuated Systems” in the revised manuscript.

2. According to Lyapunov function, the derivative of this function must be negative definite to ensure local asymptotic stability. However, the proof presented on pages 4 and 5 only demonstrates that the derivative of the chosen Lyapunov function can be constrained to a bounded number. Without specific conditions provided, it is challenging to ascertain that it is indeed negative definite. The authors should ensure that this step can be proven so that the observer's stability, as claimed, can be guaranteed.

Reply 2: Thank you very much for your constructive suggestions. It is truth, as you said, that there are problems with the previous proof. In the design process of the proposed state observer, we can choose sufficently large $l_{1}$, $l_{2}$, and $\left | l_{3} \right |$ that $\left \| P \right \|$ can be made greater than $\frac{1}{2L}$. At this point, $\dot{V}_{o}$ satisfies $\dot{V}_{o} < 0$ based on the $\dot{V}_{o} \leq (1-2L\left \| P \right \|)\varepsilon^{T}\varepsilon$. According to the Lyapunov theory, it cases the state estimate error $\varepsilon$ converges to zero exponentially fast. We have added a remark to address this solution in the revised manuscript.

3. The amplitudes in the experimental setup do not match those in the simulation. It may be necessary to ensure consistency in conditions between the simulation and the experiment.

Reply 3: Thank you very much for your insightful comment, it is a great question. In the revised manuscript, we have made it ensure consistency in conditions between the simulation and the experiment. The amplitudes of the desired reference trajectory signal are set as 180μm. Please see the simulation and experiment results in Fig.3-5 and Fig.7-8.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear Authors,

You have revised the manuscript according to my remarks and review. I have no further questions related to revised version of the manuscript. 

Kind Regards